In optical fibers, the nonlinear interaction within and between channels is primarily mediated by the intensity dependent refractive index, n2. For intensity modulation frequencies below about 1 GHz, n2 includes contributions from the electronic response of the material, n2k, as well as the electrostrictive response of the material, n2e. The electrostrictive response of the material has a strong frequency dependence, which is dependent upon the fiber geometry, material selection, and guided mode field distribution. By measuring the frequency dependence of the nonlinear refractive index, it is possible to extract a signature that enables determination of the fiber type and other properties in a deployed cable.
When a light pulse passes through an optical fiber it induces a force pushing the glass atoms toward a high intensity region in the center of the fiber. Following the light pulse, the glass relaxes and an acoustic pressure wave travels in a radial direction from the center of the fiber to the cladding boundary, where the acoustic pressure wave is partially reflected. The details of the fiber geometry, along with the material acoustic wave velocities, define resonance conditions for the transverse acoustic wave. This situation is analogous to the acoustic modes of a drum. A pulse train that is resonant with one of the acoustic modes induces a standing wave at the frequency of the pulse train. The mechanical response of the glass to light is referred to as electrostriction which produces an intensity dependent refractive index n2e that can be as much as 50% of the total intensity dependent refractive index at excitation frequencies below ˜1 GHz. A plot of the real and imaginary components of n2e(Ω) is provided in FIG. 1.
The electrostrictive response of an optical fiber can be measured from the frequency dependence of nonlinear effects, such as self phase modulation (SPM) and cross phase modulation (XPM). The strength of, n2e (Ω), is governed by the overlap integral between the radial acoustic wave eigen function and the transverse intensity distribution of the optical field in the fiber. The oscillations in n2e (Ω) diminish to extinction the spatial period of the associated acoustic modes drops below the fiber spot size. The contrast of the modes of n2e(Ω), and particularly the frequency where the contrast vanishes, is indicative of the type of fiber under test. A full derivation of n2e (Ω) is provided in the relevant art. The simulation results described herein below all assume a step index fiber geometry with a peak real component of n2e(Ω) of 1.7·10−20 W/m2 as taken from the relevant art. Recent work puts this value at ˜0.6·10−20 W/m2. Differences in the peak value rescale the results shown, but do not change the frequency dependence.
The present disclosure provides that the contrast of the frequency dependent response, which is defined as (max−min)/(max+min) as a function of eigenmode order, can be used to differentiate between fiber types and determine other fiber properties. Differences caused by overall scale factors or non-step index fiber geometries aid in fiber type classification, for example. FIG. 2 shows the frequency dependences of the real part of the nonlinear refractive index due to electrostriction for various fiber types. It is found that oscillation extinguish at lower frequencies for fibers with large core size as compared with the n2e response for small core fibers, such as true wave classic (TWC) fiber.